Your legs do stop moving when you stop the bike. Trust me. I'm in my 60s and still riding those things.

I don't know how long you've been riding but I am going to guess long enough to train in some reflexes that you will have the challenge of un-learning, especially the coast reflex when something startles you. If you are going at any speed, this will be painful (muscle pulls) and may cause a crash. There is something you can do. No, it won't help on the reflex side; that 's going to happen, but it will help big-time as far as the consequences. Really simple:

Put a piece of tape on your seatpost exactly 1/2" above the toptube (lug, collar, whatever you have). Drop the seatpost down to the tape. Yes, your seat is now way too low. But ... it will also man you cannot remotely lock your knee or even the big muscles when you do try to coast. (It will still hurt, but far less (trust me here!) and a crash is very unlikely. After a couple of these, the lesson will be learned and you can return your seatpost to that 1/2" higher (maybe going 1/4 and 1/4).

I went for my first ride 41 years ago, Used to ride with a high seat. Tried to coast to allow 3 oncoming cars by so I could turn left. I was going ~20mph. Locked my knee, got shot in the air and collapsed on the road with minor bruises, virtually no road rash (I converted my 20mph into vertical speed). Felt like I put my left leg through a shredder. A shredder that left the skin intact.

But I returned from that ride sold! I've always had a fix gear since and just over half my miles since have been ridden fixed.

Fix gears are time machines. They take you to cycling at its purist. There is nothing like them. And they have the additional feature of conditioning you more/faster when you have to limit your miles or time on the bike. Plus they are just plain fun! Never get boring. I often go the garage to ride my geared bikes, get out to the road and turn around and change bikes and shoes just because fixed sounds like more fun.

Ben